Patent GB-430003-A (GB)
Title: Unsymmetrical electric wave filters
IPC: H03H7/01
Filed: 1933-11-08
Abstract: 430,003. Impedance networks. CAUER, W., 67, Calsowstrasse, G÷ttingen, Germany. Nov. 8, 1933, No. 31132. Convention date, Nov. 10, 1932. Drawings to Specification. [Class 40 (iii)] The method of designing symmetrical filters described in Specifications 350,498<*> and 396,084 is now extended to unsymmetrical filters, and particularly to those which (i) are unsymmetrical in the suppression regions but approximately symmetrical in the transmission regions, so that the image impedances are for the latter regions approximately equal to the same resistance R (through they may be equal to two different constant resistances) ; and (ii) are "C-D" filters, so that the determinant of the characteristic matrix of their open-circuit impedances is equal to R<2>. The Specification considers the case of a symmetrical filter, Figs. 1 and 2 (not shown), whose two halves, in themselves unsymmetrical, are mirror images of one another; such a filter is selected so that it belongs to one of the Cauer classes defined in Specification 350,498<*> by applying the theorem that if the elements of the matrix are to be the open-circuit impedances of a four-terminal reactance network, then the expression Z11 J1<SP>2>+2Z12J1J2+J22J2<SP>2> must, for all pairs of real values of J1' J2, behave as the impedance of a two-terminal reactance network. From this principle the general forms of Z11' Z12' Z22, are deduced. The Specification next considers the image impedances W1, W2, of the filter under construction, and also a quantity D such that D = #(z11z22 /#) where z11=Z11/R, z22=z22/R, and R<2># is the determinant of the above matrix. The quantities W1, W2 and D are arbitrarily selected from the Cauer classes already referred to and Z11' Z22are then chosen as W1D, W2D respectively while R<2># or (Z11Z22- Z12<SP>2>) is found to be equal to W1W2. The Specification proceeds to examine the conditions under which the value of Z12 deduced from these equations is compatible with the conditions of the problem. The special case of C-D filters, i.e. filters for which #=1, is considered and it is shown that #Z12 must in this case be a real and rational function of # where #=jw and w is the pulsatance of the applied oscillations. The Specification next gives tables showing classes of functions, similar to the Cauer classes already mentioned, from which D and W1 may be chosen ; W2 can then be deduced from the relation W1W2 = R<2>. As in the known Cauer classes, the formulae in these tables contain arbitrary parameters Á, m, wa &c., which have to be selected in accordance with the conditions of the problem. They are chosen to be T parameters, which closely resemble the Tschebyscheff parameters described in Specification 396,084. Tschebyscheff parameters are such that over a defined range of frequency the quantity #(Z11Z22) oscillates between determinate upper and lower limits whose geometric mean is unity. T parameters, on the other hand, are so chosen that the upper one of these limits is unity, Fig. 4 (not shown). The Specification gives tables of T parameters, and defines a notation for indicating the classes of function determined by these parameters. A filter for which the attenuation characteristic D belongs to the T class denoted by y /2 while its image impedance W1 belongs to the class denoted by 2 is specified as " gamma/2,2 ". While D must have T parameters, W1 may have Tschebyscheff parameters. The manner in which the physical construction of the required filter is to bo deduced from the functions thus selected is shown in the Specification by means of a numerical example, Fig. 3 (not shown).